Pull a cart shakily after a race (7)
I believe the answer is:
attract
'pull' is the definition.
(attracting is a kind of pulling)
'a cart shakily after a race' is the wordplay.
'shakily' indicates anagramming the letters.
'after' is a charade indicator (letters next to each other).
'race' becomes 'tt'.
'cart' is an anagram of 'ract'.
'a'+'tt'='att'
'ract' after 'att' is 'ATTRACT'.
(Other definitions for attract that I've seen before include "Draw, pull" , "Entice" , "to be appealing" , "Arouse interest of" , "Act as a magnet" .)